I had Ubuntu installed before (dual boot WinXP/Ubuntu), but it was completely useless because I know how to use Windows well. Linux is honestly not for me, I tried it and hated it. I already had Microsoft Word (it's good software, just over priced), and OpenOffice just didn't cut it for me. I do a lot of creative things (like Photoshop, video editing, etc.), and Ubuntu just ddin't cut it. I had all of my documents, software, porn, and other stuff on my Windows partition, and maintaining two OS's was too hard. Did I mention how freakin' hard it was to delete the Ubuntu partition and allow Windows to use that space?

No, if you install Linux on your external HDD then you'll be able to boot it on your computer -- unless it's a portable version of Linux. The reason is, there are drivers and configuration files that are designed around your system. Trying to boot on a different system will obviously have the wrong settings/configurations than your own machine.

If you install Linux onto an external HDD it will work on other computers if they can boot from the external HDD. You will have problems in the form of no GUI if the graphic card chip is very different (like ATI instead of Nvidia), but there are some standard drivers you could use for the x-server that work on many different systems. Drivers shouldn't be an issue because the Linux kernel decides itself what drivers are needed as far as I know (but I'm no expert), and common distributions pack all common drivers into the kernel. I've installed Ubuntu 7.04 on an external HD myself before and had said GUI issues, but it booted and I was able to do what I wanted to do (make a HDD backup). I also got the x-server running again, but you'd have to make an extra config for every PC you want to boot it on.

It's a wild guess, but maybe mm3 was talking about the HDD config that might get messed up. New linux distributions usually do this right, but if you are getting a linux made for this purpose anyway you won't have the config issues described I guess